The Andrew & Erna ViterbiFaculty of Electrical Engineering

Signal Acquisition Modeling and Processing Lab

Avinoam Bar-Zion*1, Martino Alessandrini2, Jan D'hooge2, Dan Adam1 and Yonina Eldar3

1 Department of Biomedical Engineering, Technion, Haifa, Israel. 2 Department of Cardiovascular Sciences , KU Leuven, Leuven, Belgium. 3 Department of Electrical Engineering, Technion, Haifa, Israel.

Towards Sub-Nyquist Tissue Doppler Imaging

Tissue Doppler Imaging

Results

Current Technology

Methods

Motivation

Conclusion

References

Tissue Doppler imaging (TDI) facilitates quantification of LV function by estimating the myocardial velocity profile Currently: few measurement points through the LV [1]

Tradeoff between spectral and spatial resolutionThe received A-ling signals (fast time) are sampled at frequencies higher than the Nyquist rate

M Consecutive Pulses Are

Transmitted and Received

fasttime

slowtime

Demodulation + Low Pass Filter

Analog to Digital Conversion and Beamforming

Short Time Fourier Transform

time

frequency

646804-BNYQ

This project has received funding from the European Union's Horizon 2020 research and innovation

programme under grant agreement No. 646804-ERC-COG-BNYQ

Non-Uniformly Spaced Pulses

Estimating the Fourier Coefficients

Sampling rate reduction via CS

Validation

Non-Uniformly Spaced Stream of Pulses is transmitted:

The received signal from L dominant scatterers is defined by the 3L degrees of freedom (DOF):The received A-line reflected from L scatterers:

The Fourier series representation of a single A-line is [2]:

The representation matrices present the velocities at different depths:

With 20% of the pulses the map’s correlation coef. R > 0.8

Spectral estimations from specific depths can be concatenated to produce spectral Doppler images

The proposed signal model was supported by our resultsTDI signals can be reconstructed from sub Nyquist samples:

• Only subset of the fast time frequencies are used• Non-uniformly space stream of pulses transmitted

Time gaps between pulses can be used for scanning in different directions Current performance is satisfactory, and can still be improvedFuture research directions includes:

• Extension to vector Doppler• Extension to color Doppler• Optimization of the reconstruction algorithm and the selection of transmitted pulses

1. T. H. Marwick, C. Yu, J. P. Sun, Myocardial Imaging: Tissue Doppler and Speckle Tracking,” 2007.

2. D. Cohen, A. Dikopoltsev and Y. C. Eldar, "Extensions of Sub-Nyquist Radar: Reduced Time-on-Target and Cognitive Radar," 2015.

3. M. Mishali, Y. C. Eldar, O. Dounaevsky, and E. Shoshan, “Xampling: Analog to digital at sub-Nyquist rates,” 2011.

4. T. Chernyakova, Y.C. Eldar, “Fourier Domain Beamforming: The Path to Compressed Ultrasound Imaging,” 2014.

5. M. Alessandrini et al. , “A Pipeline for the Generation of Realistic 3D Synthetic Echocardiographic Sequences: Methodology and Open-Access Database,” 2015.

Compression+Sampling = Xampling [3] Fourier coefficients can be estimated following pre-filtering

Multi element transducer: Compressed Beamforming - beamforming in the Fourier Domain on low rate samples [4]

Using synthetic echocardiographic sequences[5]Geometries extracted from 3D ultrasound scans

A demo version was implemented on a Verasonics Vantage 256™ system

The system of equations :

The sparse representation matrix A is estimated from the measurements by solving the l1 minimization problem:

Representation

Slow time sub-Nyquist: contains P out of the M rows of the DFT matrix

100% Slow Time40% Fast Time

50% Slow Time40% Fast Time

20% Slow Time40% Fast Time

Fast time sub-Nyquist: contains K out of the N rows of the DFT matrix

Under-determined system of equations

Depth-Doppler Maps - Quantification

TDI Plots

Thanks!We thank Regev Cohen, Shai Yagil, Ido Cohen and Ariel Rosenberg for their work on the demo. We also thank Verasonics for their support.

Depth = 6.2 cm; 40% fast time